Abstract
BackgroundUnderstanding the structure of complex networks is a continuing challenge, which calls for novel approaches and models to capture their structure and reveal the mechanisms that shape the networks. Although various topological measures, such as degree distributions or clustering coefficients, have been proposed to characterize network structure from many different angles, a comprehensive and intuitive representation of large networks that allows quantitative analysis is still difficult to achieve.Methodology/Principal FindingsHere we propose a mesoscopic description of large networks which associates networks of different structures with a set of particular curves, using breadth-first search. After deriving the expressions of the curves of the random graphs and a small-world-like network, we found that the curves possess a number of network properties together, including the size of the giant component and the local clustering. Besides, the curve can also be used to evaluate the fit of network models to real-world networks. We describe a simple evaluation method based on the curve and apply it to the Drosophila melanogaster protein interaction network. The evaluation method effectively identifies which model better reproduces the topology of the real network among the given models and help infer the underlying growth mechanisms of the Drosophila network.Conclusions/SignificanceThis curve-shaped description of large networks offers a wealth of possibilities to develop new approaches and applications including network characterization, comparison, classification, modeling and model evaluation, differing from using a large bag of topological measures.
Highlights
Networks have been widely used as a concise mathematical representation of the structure of systems with interacting objects [1,2,3,4]
The results suggest that the Duplication-mutation using random mutations model (DMR) model better reproduces the topology of Drosophila’s network than the Duplication-mutation-complementation model (DMC) and Linear preferential attachment model (LPA) for high confidence thresholds PÃc~0:65=0:5
This result is completely opposite to the result achieved by a method based on subgraph census [29], which suggests that the DMC best reproduces Drosophila’s network among seven candidate models, including the DMR and LPA
Summary
Networks have been widely used as a concise mathematical representation of the structure of systems with interacting objects [1,2,3,4]. Real-world networks studied in recent years often involve thousands or millions of vertices and edges Networks on this scale cannot be represented in a way that allows quantitative analysis to be conducted by eye [5]. A good description or representation of network which holds more complete topological information in one bag may provide a clear intuitive understanding of network and reflect some special structural features, such as the curved landscape of the World Wide Web [12], cartographic representation of complex networks [13] and circular perspective drawings of protein interaction networks [14]. Various topological measures, such as degree distributions or clustering coefficients, have been proposed to characterize network structure from many different angles, a comprehensive and intuitive representation of large networks that allows quantitative analysis is still difficult to achieve
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